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Properties

Label 7098.b
Number of curves $1$
Conductor $7098$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve([1, 1, 0, -16981799, -27096574539]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 7098.b1 has rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 + T\)
\(7\)\(1 - T\)
\(13\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 + 3 T + 5 T^{2}\) 1.5.d
\(11\) \( 1 + T + 11 T^{2}\) 1.11.b
\(17\) \( 1 - 7 T + 17 T^{2}\) 1.17.ah
\(19\) \( 1 + T + 19 T^{2}\) 1.19.b
\(23\) \( 1 + 7 T + 23 T^{2}\) 1.23.h
\(29\) \( 1 - 3 T + 29 T^{2}\) 1.29.ad
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 7098.b do not have complex multiplication.

Modular form 7098.2.a.b

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 3 q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 3 q^{10} - q^{11} - q^{12} - q^{14} + 3 q^{15} + q^{16} + 7 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 7098.b

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.b1 7098d1 \([1, 1, 0, -16981799, -27096574539]\) \(-112205650221491190337/745029571313664\) \(-3596115440082935218176\) \([]\) \(799680\) \(2.9718\) \(\Gamma_0(N)\)-optimal